Thermohydrodynamic instabilities of conducting liquid jets in the presence of time-dependent transverse electric fields

A novel system to study the effect of time-dependent radial electric fields on the stability of a cylindrical interface between the vapor and liquid phases of conducting fluids in the presence of heat and mass transfer is investigated. The vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relation is obtained and discussed, for the periodic electric field case, and the stability of the system is analyzed theoretically and numerically. Both the nonresonant and resonant cases are considered. Using the multiple time scales method, we found that the obtained dispersion relation is the damped Mathiew equation with real coefficients. Both the frequency of the periodic electric field and the dimensions of the system are found to have stabilizing effects, while both the azimuthal wavenumber and the electrical conductivity have destabilizing effects; and the heat and mass transfer are found to have no effect on the stability of the system. The behavior of the resonance points (increased, or decreases, or a steady) corresponding to the above physical parameters are determined.